Advanced Methods in Quantitative Finance

This course is designed for students and researchers who want to develop professional skills in modern quantitative finance. It is offered to interested students who have had some experience with probability, statistics and software applications but have not had advanced courses in mathematical finance. Although the course assumes only a modest background it moves quickly between different fields of applications and in the end, the participant can expect to have theoretical and computational tools that are deep enough and rich enough to be relied on throughout
future professional careers. The course starts with an introduction into the basic concepts of value at risk, option pricing and its probabilistic foundations. Next, numerical solutions via a binomial or trinomial tree construction will be discussed in detail. Modern financial engineering techniques such as the Implied volatility (IV) models or State Pricing Densities estimation will be also discussed as approaches to resolve a shortcoming of the BS model.